Possible Duplicates:
Random weighted choice
Generate random numbers with a given (numerical) distribution

I have a list of list which contains a series on numbers and there associated probabilities.

prob_list = [[1, 0.5], [2, 0.25], [3, 0.05], [4, 0.01], [5, 0.09], [6, 0.1]]

for example in prob_list[0] the number 1 has a probability of 0.5 associated with it. So you would expect 1 to show up 50% of the time.

How do I add weight to the numbers when I select them?

NOTE: the amount of numbers in the list can vary from 6 - 100

EDIT

In the list I have 6 numbers with their associated probabilities. I want to select two numbers based on their probability.

No number can be selected twice. If "2" is selected it can not be selected again.

I'm going to assume the probabilities all add up to 1. If they don't, you're going to have to scale them accordingly so that they do.

First generate a uniform random variable [0, 1] using random.random(). Then pass through the list, summing the probabilities. The first time the sum exceeds the random number, return the associated number. This way, if the uniform random variable generated falls within the range (0.5, 0.75] in your example, 2 will be returned, thus giving it the required 0.25 probability of being returned.

import random
import sys
def pick_random(prob_list):r, s = random.random(), 0for num in prob_list:s += num[1]if s >= r:return num[0]print >> sys.stderr, "Error: shouldn't get here"

Here's a test showing it works:

import collections
count = collections.defaultdict(int)
for i in xrange(10000):count[pick_random(prob_list)] += 1
for n in count:print n, count[n] / 10000.0

which outputs:

1 0.498
2 0.25
3 0.0515
4 0.0099
5 0.0899
6 0.1007

EDIT: Just saw the edit in the question. If you want to select two distinct numbers, you can repeat the above until your second number chosen is distinct. But this will be terribly slow if one number has a very high (e.g. 0.99999999) probability associated with it. In this case, you could remove the first number from the list and rescale the probabilities so that they sum to 1 before selecting the second number.